{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 回忆我们之前的例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.empty((100,2))\n",
    "X[:,0] = np.random.uniform(0., 100., size=100)\n",
    "X[:,1] = 0.75 * X[:,0] + 3. + np.random.normal(0, 5, size=100)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)\n",
    "X_reduction = pca.transform(X)\n",
    "X_restore = pca.inverse_transform(X_reduction)\n",
    "plt.scatter(X_restore[:, 0], X_restore[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从图1到图2有信丢失了，丢失的这部分信息中很有可能有很大一部分是噪声\n",
    "降维的过程中丢失了信息，同时也去除了部分噪音"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 手写识别例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "digits = datasets.load_digits()\n",
    "X = digits.data\n",
    "y = digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "noisy_digits = X + np.random.normal(0, 4, size=X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "example_digits = noisy_digits[y == 0, :][:10]\n",
    "for num in range(1, 10):\n",
    "    X_num = noisy_digits[y==num,:][:10]\n",
    "    example_digits = np.vstack([example_digits, X_num])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    #fig, axes = plt.subplots(10, 10, figsize=(10, 10), subplot_kw={'xticks':[], 'yticks':[]},girdspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    fig, axes = plt.subplots(10, 10, figsize=(10, 10), subplot_kw={'xticks':[], 'yticks':[]})\n",
    "    for i,ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8), cmap='binary', interpolation='nearest', clim=(0,16))\n",
    "    plt.show()\n",
    "\n",
    "plot_digits(example_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=0.5, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.5)\n",
    "pca.fit(noisy_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "components = pca.transform(example_digits)\n",
    "filtered_digits = pca.inverse_transform(components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(filtered_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
